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Grade 12Integral Calculus

intagrate x⁵^/2dx=alog( x^k)

x^7/6+x⁶(1+x^k)

sneha sunil raikar

17 Years agoGrade 12

1 Answer

Jitender Singh

12 Years ago

Ans: 5/2

$I = \int \frac{x^{5/2}}{x^{6}+x^{7/2}}dx$

$t = \sqrt{x}$

$dt = \frac{1}{2\sqrt{x}}dx$

$I = 2\int \frac{1}{t(t^{5}+1)}dt$

$s = t^{5}$

$ds = 5t^{4}dt$

$I = \frac{2}{5}\int \frac{1}{s(s+1)}ds$

$I =\frac{2}{5}log(\frac{s}{s+1}) +constant$

$I =\frac{2}{5}log(\frac{t^{5}}{t^{5}+1}) +constant$

$I =\frac{2}{5}log(\frac{x^{5/2}}{x^{5/2}+1}) +constant$

k = 5/2

Thanks & Regards

Jitender Singh

IIT Delhi

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